If you ask 10 furries that question, you'll receive 10 different answers.
For myself and most of the furries I know, the answer is community. The furry fandom is where you're fans of each other (other furries). Your fursona is how you express yourself in an environment where self-acceptance and self-love is emphasized. What you make of that opportunity is a personal choice.
Why be a part of that? Because it's good, wholesome fun, and strangely liberating.
It might seem weird, but weird doesn't mean bad. Embrace your weirdness.